Gauss theorem and the nature of the surface

In summary, according to Gauss’ law, the total number of lines of force over a closed surface is equal to 1/ε times the net charge enclosed within the closed surface. This is because only a closed surface can enclose a charge and accurately calculate the flow of lines of force. The idea of a specific number of lines of force is an abstract concept and does not have a physical meaning. The quoted value of 1.129 x 10[SUP]11 lines of force for 1 C of charge in air or vacuum is not accurate and varies depending on units used. It is important to note that the concept of "lines of force" is a problematic one and should not be relied upon for accurately calculating electric flux.
  • #1
ananthu
106
1
According to Gauss’ law the total number of lines of force over a closed surface is equal to 1/ε times the net charge enclosed within the closed surface. Why should it be a closed surface but not an open surface too? I am unable to find a convincing explanation for it. Since we take into account only the number of lines starting or reaching a charge, the total number of lines is not going to vary whether we take a closed surface or open surface near the charge. Then why should it be specifically a closed one? Can anyone giving a convincing explanation?
 
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  • #2
If the surface is open, you can get any arbitrary value. It is important that you enclose the whole mass - without leaks, so to speak.
There is no "number of lines of force".
 
  • #3
mfb said:
If the surface is open, you can get any arbitrary value. It is important that you enclose the whole mass - without leaks, so to speak.
There is no "number of lines of force".
Thank you for the reply. If there is no lines of force, then how the calculated value of 1.129 x 1011 lines of force from 1 C of charge placed in air or vacuum arrived? What does that number exactly stand for? The value has been obtained from the formula 1/ε for air.
 
  • #4
I am by means an expert but, what Gaus law does is to collect all that flows through a surface. If you don't totally enclose the charge there will be flow going out that you are not calculating.
 
  • #5
Because only a closed surface can enclose a charge.

How do you define "enclosed charge" when your surface is open?
 
  • #6
ananthu said:
If there is no lines of force, then how the calculated value of 1.129 x 1011 lines of force from 1 C of charge placed in air or vacuum arrived?
I have no idea who did that, but it is wrong.
What does that number exactly stand for?
Nothing.
$$\frac{1C}{\epsilon_0}=1.13\times 10^{11} Vm$$
The numerical value depends on the units you use - if you convert this to imperial units, you get a different number, for example. This alone shows that the numerical value itself cannot have a physical meaning (like some number of "lines").
 
  • #7
mfb said:
I have no idea who did that, but it is wrong.

This value has been given in the XII std physics textbook published by Tamil Nadu (India) government.

One of the properties of the electric lines of force given in the book is: "each unit positive charge placed in free space gives rise to 1/ ε lines of force, which works out to be equal to the quoted value taking ε for air as 8.854x10-12.

Though I could understand that the lines of force is merely an imaginary concept to visualize the electric flux, I find it difficult to convincingly explain how such an exact number could be specified when no one can count the number of lines of force as such, coming out of a closed area since such an idea is purely an abstract one. I will be happy if you could come out with a more convincing reply.
 
  • #8
It is pointless to talk about a "number of lines of force". Such a thing does not exist.
I think "line of force" itself is a problematic concept, but at least it has some clear meaning (=field lines). Let's look at the points 1m away from a charge: Every point is on its own "line of force", and the number of points in a distance of 1m is infinite. There is no way to get any finite number for "lines of force". If you want to draw them, you have to restrict yourself to a finite number, but that is not an exact drawing of the field.
 

1. What is Gauss theorem?

Gauss theorem, also known as the divergence theorem, is a fundamental theorem in vector calculus that relates the flux of a vector field through a closed surface to the divergence of the vector field within the enclosed volume.

2. What is the significance of Gauss theorem in science?

Gauss theorem is important in many areas of science, including fluid mechanics, electromagnetism, and heat transfer. It provides a powerful tool for solving problems involving vector fields and their behavior within a given volume.

3. How is Gauss theorem related to the nature of the surface?

Gauss theorem relates the flux of a vector field through a closed surface to the divergence of the vector field within the enclosed volume. This means that the nature of the surface, such as its shape or orientation, can affect the behavior of the vector field and the resulting flux through the surface.

4. Can Gauss theorem be applied to any surface?

Yes, Gauss theorem can be applied to any closed surface, regardless of its shape or orientation. This makes it a versatile tool for solving problems in various scientific fields.

5. How is Gauss theorem used in real-world applications?

Gauss theorem has a wide range of applications in various fields, such as calculating the flow of fluids through pipes, determining the electric field inside a charged object, and predicting the temperature distribution in a heated object. It is also used in computer simulations and engineering designs to analyze and optimize systems.

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